We will use the law of conservation of linear momentum in this problem.

$\overline{)\begin{array}{rcl}{\mathbf{m}}_{\mathbf{b}}{\mathbf{v}}_{\mathbf{b}\mathbf{0}}\mathbf{+}{\mathbf{m}}_{\mathbf{r}}{\mathbf{v}}_{\mathbf{r}\mathbf{0}}& {\mathbf{=}}& {\mathbf{m}}_{\mathbf{b}}{\mathbf{v}}_{\mathbf{b}\mathbf{f}}\mathbf{+}{\mathbf{m}}_{\mathbf{r}}{\mathbf{v}}_{\mathbf{r}\mathbf{f}}\end{array}}$.

Here, b stands for blue cart and r for the red cart.

From the conservation of kinetic energy, which is always the case for a perfectly elastic collision, we have:

$\overline{)\begin{array}{rcl}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}_{\mathbf{b}}{{\mathbf{v}}_{\mathbf{b}\mathbf{0}}}^{\mathbf{2}}& {\mathbf{=}}& \frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}_{\mathbf{b}}{{\mathbf{v}}_{\mathbf{b}\mathbf{0}}}^{\mathbf{2}}\mathbf{+}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}_{\mathbf{r}}{{\mathbf{v}}_{\mathbf{r}\mathbf{f}}}^{\mathbf{2}}\end{array}}$

A blue cart (mass=0.400kg) makes an elastic collision with a red cart (mass=0.750kg). The blue cart is initially moving at 1.40 m/s to the right before the collision, and the red cart is intially at rest. What are the final velocities of the blue and red carts (magnitude and direction)? How much kinetic energy is lost in the collision?

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